Hybrid system identification is a key tool to achieve reliable models of Cyber-Physical Systems from data. PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. Still, PWA identification is a challenging problem, requiring the concurrent solution of regression and classification tasks. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX), thus not restricted to polyhedral domains, and characterized by discontinuous maps. To this end, we propose a method based on a probabilistic mixture model, where the discrete state is represented through a multinomial distribution conditioned by the input regressors. The architecture is conceived following the Mixture of Expert concept, developed within the machine learning field. To achieve nonlinear partitioning, we parametrize the discriminant function using a neural network. Then, the parameters of both the ARX submodels and the classifier are concurrently estimated by maximizing the likelihood of the overall model using Expectation Maximization. The proposed method is demonstrated on a nonlinear piece-wise problem with discontinuous maps.

中文翻译：

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识别具有任意域的概率加权 ARX 模型

混合系统识别是从数据中获得可靠的信息物理系统模型的关键工具。PieceWise Affine 模型保证通用逼近、局部线性以及与其他类别混合系统的等效性。尽管如此，PWA 识别仍然是一个具有挑战性的问题，需要同时解决回归和分类任务。在这项工作中，我们专注于使用具有任意区域的外源输入模型 (NPWARX) 识别 PieceWise 自回归，因此不限于多面体域，并以不连续映射为特征。为此，我们提出了一种基于概率混合模型的方法，其中离散状态通过输入回归量条件的多项式分布来表示。该架构是按照混合专家概念构思的，在机器学习领域开发。为了实现非线性分区，我们使用神经网络参数化判别函数。然后，通过使用期望最大化来最大化整个模型的似然，同时估计 ARX 子模型和分类器的参数。在具有不连续映射的非线性分段问题上演示了所提出的方法。